No abstract

Nonlinear evolution differential equations with unbounded linear operators of disturbance by Gaussian random processes are considered in an abstract Hilbert space. For the Cauchy problem for the differential equations, the sufficient existence and uniqueness conditions for their solutions are proved and the sufficient conditions for the equivalence of the probability measures generated by these solutions are derived. Moreover, the corresponding Radon-Nikodym densities are calculated explicitly in terms of the coefficients or characteristics of the considered differential equations. Keywords: evolution differential equations, evolution family of bounded operators, Radon-Nikodym density, equivalence of probability measures, generating operator, Hilbert-Schmidt operator.Applied scientific and engineering problems are known to involve differential equations with random terms or coefficients that describe the behavior of systems in random media. The solutions of such equations obviously generate probability measures in infinite-dimensional spaces.One of the major problems in the theory of random processes is to establish the sufficient conditions for the equivalence of the above-mentioned probability measures with respect to some standard well-studied measures and to explicitly determine the corresponding Radon-Nikodym densities, naturally, in terms of known quantities, and in our case, in terms of the coefficients of the equations under study, their characteristics or abstract transformations. The existence of such densities allows an efficient solution of applied problems with the use of integration over known standard distributions (for example, Gaussian, Wiener, etc.) for which algorithms are available.The publications [1-42] address the absolute continuity and equivalence of probability measures for different classes of nonlinear transformations and nonlinear differential equations with Gaussian perturbation, which were applied to calculate optimal estimates in extrapolation and filtration problems for the solution of the differential equations [7,8,12,[34][35][36][37][38][39].The present paper can be considered as a continuation of the studies in this field for nonlinear evolution differential equations in a Hilbert space H and of the studies initiated in [44] for random fields being the solutions of Dirichlet and Neumann boundary-value problems for nonlinear elliptic differential equations in a finite-dimensional Euclidean space.In contrast to the previous studies, we will consider, for the first time, nonlinear differential equations with unbounded linear operators, which are a family of generating operators for the evolution family of bounded operators. We will use the concept of extended stochastic integral and the results from [9] to establish the sufficient conditions for the equivalence of the probability measures under study and to calculate explicitly the corresponding Radon-Nikodym densities.Denote by { } W, , Ã P a fixed probability space and by H a real separable Hilbert space with scalar product ( ,...

Documentary support of internal control of transactions with current assets has been considered in the article. The objective of the article is to summarize documentation of internal control of transactions with current assets and to present the forms of work papers of an internal controller for the object in order to improve organization and methods of internal control. This study of internal control documentation of current assets was conducted using methods of analysis, generalization, grouping and comparison. The method of graphical representation was applied in the development of certain forms of work papers. It is established that at present there is no legislative regulation of the procedure for documenting internal control, which, on the one hand, complicates the activities of internal controllers, and on the other hand, it gives some autonomy in the selection and application of specific documents. Documenting internal control of transactions with current assets through the use of organizational and preparatory, working and final reporting documentation will enable achieving the objectives in the most efficient, effective and economical way for the entity. Twenty forms of work papers of the internal controller on transactions with current assets have been developed, namely on verification of: composition and structure of current assets; checking the composition and share of individual stocks in current assets; correctness of the assignment of certain types of stocks to the relevant accounts; correctness of the formation of initial cost of certain types of stocks; correctness of the value of inventories in line 1100 "Inventories" of the Balance Sheet (Statement of financial situation) of an enterprise; composition and structure of current biological assets; correct entry of animal crop; composition and share of receivables in current assets; correctness of the formation of data on receivables and analysis of its structure; terms and ways of occurrence of receivables; comparison of the amount of receivables with the data of the counterparty; grouping of receivables by maturity; assessment of the state of contractual discipline and methods of influencing debtors; correctness of registration of transactions with accountable persons; completeness and timeliness of reporting of accountable persons (separately for each accountable person); the order of accounting for current financial investments; composition and structure of money and their equivalents; procedure for accounting for future expenses; composition and structure of other current assets; availability and procedure for the formation of amounts under additional items of current assets of the Balance Sheet (Statement of financial situation) and a letter of request sent to the counterparty to confirm the reality of receivables. The presented work papers are part of the methodological support of internal control of certain current assets. Their practical use in the activities of internal controllers will allow obtaining, investigating, summarizing, grouping and visualizing information about the actual state of the object under study. Prospects for further research are seen in the deepening of the scientific component of documentation of internal control, development of document classification for the subjects of control powers and presentation of forms of work papers for various objects.

The paper attempts to describe a number of linguistic and pragmatic aspects of modeling the anti-Russian discourse in the English language media headlines. The authors focus on the coverage of the Skripal poisoning case and the specific language means employed by a range of English-language news sources, such as The Guardian, BBC, CNN, Politico, The Mirror, The Daily Mail, The New Zealand Herald, The Herald. The results of the study indicate that one of the most effective and widespread media manipulation techniques is misinformation accompanied by a discrepancy between the headline and the content of the article. The research seeks to classify manipulation techniques according to the way of their actualization in the language and the degree of misinformation: full fabrication, partial fabrication, manipulated content, selective quoting, false connection, emphasizing communication relevant elements by means of the actual division of the sentence. The implementation of such manipulation techniques is aimed at shaping public opinion on the incident at issue in order to promote a negative image of Russia and its leader in terms of their alleged involvement in the Skripal attack.

The problem of forecasting the time series of stock prices of leading global companies that are characterized by long-term memory is considered. It is assumed that ignoring the presence of such a correlation structure in time series using traditional methods of analysis leads to a much greater error than taking into account long-term memory in its actual absence. It is assumed that the daily fluctuations in prices for financial market instruments are the Hurst process, that is, they have long-term memory, which means such a time series cannot be effectively analyzed using traditional stationary models that completely ignore this fact. Thus, the task is set, using the R / S-analysis method, to determine the presence of long-term memory in the initial time series and to determine its type.