Remarks on the existence and uniqueness of the solutions to stochastic functional differential equations with infinite delay

Abstract

In this paper, we obtain some results on the existence and uniqueness of solutions to stochastic functional differential equations with infinite delay at phase space BC((−∞, 0]; R d ) which denotes the family of bounded continuous R d -value functions defined on (−∞, 0] with norm = sup −∞< 0 | ( )| under non-Lipschitz condition with Lipschitz condition being considered as a special case and a weakened linear growth condition. The solution is constructed by the successive approximation.

To Build an Optimization Model of Biomedicine Regression Analysis Decision and a Study of Its Application

“…is conditional probability of disease 1 D on the condition that symptom kj S has been known. If we define…”

“…If combined with the concrete problem in practice, it is a practical experiential expression which is often of theoretical or practical value. This essay discusses how to set up the kind of important mathematics model in the scope of biology and medicine, and then goes further into the discussion about the practical application of regression expression in biology calculation [1][2] .…”

Caratheodory's approximate solution to stochastic differential delay equation

“…In [7], Ren et al considered the following d-dimensional stochastic functional differential equations: …”

“…2) can be written as the equation (2.1) and so one can apply the existence and uniqueness theorem established in [7] to the delay equation (2.2). Now, we need the following lemmas in order to show the main results:…”

“…n } stands for the Lebesgue measure on R. For some more details on stochastic differential equations, refer to [1][2][3][5][6][7][8][9][10][11] and references therein. By using the nonlinear growth condition and nonlinear growth condition, in 2015, Kim [4] studied the difference between the approximate solution and the accurate solution to the stochastic differential delay equation (shortly, SDEs).…”