On the Convergence of Ordinary Integrals to Stochastic Integrals

Wong, Eugene; Zakai, Moshe

doi:10.1214/aoms/1177699916

Cited by 610 publications

(378 citation statements)

References 1 publication

Supporting

Mentioning

365

Contrasting

Unclassified

Order By: Relevance

“…In this sense our method gives approximations tending toward the correct solution, and it is possible to obtain an approximation of any required accuracy by letting z.t be small. For the mathematical theory, readers may refer to Storokhod (1965), Wong andZakai (1965), andMcShane (1974). There are several other simulation methods (Bailey etal.…”

Section: Mathematical Methodsmentioning

confidence: 99%

Numerical studies of the frequency trajectories in the process of fixation of null genes at duplicated loci

Maruyama

Takahata

1981

Heredity

View full text Add to dashboard Cite

A new numerical method, based on the stochastic differential equations, has been applied to the problem of the fixation of null alleles at duplicated loci. The results reported here were obtained under the assumption that individuals carrying homozygous null genes at both of the duplicated loci are lethal, but all the other genotypes are normal. The mean and median time for null alleles to fix can vary from 2N to lOON or more, depending on the mutation rate and the population size, where N is the population size. Linkage has strong effects on the fate of null genes in the populations, if 2Nc is of the order of 100 or less (c = recombination value). When the linkage is loose the frequencies of null genes in the course of fixation stay in a region where the frequency of the null gene is very low at one of the two duplicated loci. If the two loci are tightly linked, the fate of null genes at duplicated loci is determined by the mutation pressure and the random genetic drift, and selection plays a minor role. In these cases, the fixation time is invariably reduced and the trajectories can cover the entire region where the sum of null allele frequencies does not exceed unity. This makes the prediction that there should be rapid evolution of linked silent genes and pseudo-genes, and that silent DNA might be found close to functional genes.

show abstract

Section: Mathematical Methodsmentioning

confidence: 99%

Numerical studies of the frequency trajectories in the process of fixation of null genes at duplicated loci

Maruyama

Takahata

1981

Heredity

View full text Add to dashboard Cite

show abstract

“…expressed in the time-symmetric (Stratonovich) picture [12,13] where dρ/dt ≡ lim δt→0 [ρ(t + δt) − ρ(t − δt)]/2δt. We now examine the requirements for time-reversal symmetry of Eq.…”

Section: Continuous Time Symmetrymentioning

confidence: 99%

Janus sequences of quantum measurements and the arrow of time

Jordan

Chantasri

Murch³

et al. 2017

AIP Conference Proceedings

View full text Add to dashboard Cite

Abstract. We examine the time reversal symmetry of quantum measurement sequences by introducing a forward and backward Janus sequence of measurements. If the forward sequence of measurements creates a sequence of quantum states in time, starting from an initial state and ending in a final state, then the backward sequence begins with the time-reversed final state, exactly retraces the intermediate states, and ends with the time-reversed initial state. We prove that such a sequence can always be constructed, showing that unless the measurements are ideal projections, it is impossible to tell if a given sequence of measurements is progressing forward or backward in time. A statistical arrow of time emerges only because typically the forward sequence is more probable than the backward sequence.

show abstract

“…If t h e system were completely aa There are two c a s e s i n which ( 3 ) , ( 4 ) and ( 3 ) can b e immediately checked. One i s t h e completely l i n e a r -g a u s s i a n case, t h e o t h e r i s t h e case where f = 0 and V = 0 ( n o dynamics).…”

Section: T ' Of T H E C O N D I T I O N a L Process Xmentioning

confidence: 99%