Consider the following distribution dependent SDE: dXt=?t(Xt,?Xt)dWt+bt(Xt,?Xt)dt, where ?Xt stands for of Xt. In this paper non-degenerate ?, we show strong well-posedness above SDE under some integrability assumptions in spatial variable and Lipschitz continuity ? about b ?. particular, extend results Krylov–Röckner (Probab. Theory Related Fields 131 (2005) 154–196) to case.

Stochastic differential equations (SDEs) provide accessible mathematical models that combine deterministic and probabilistic components of dynamic behavior. This article is an overview of numerical solution methods for SDEs. The solutions are stochastic processes that represent diffusive dynamics, a common modeling assumption in many application areas. We include a description of fundamental nu...

The conformational transition pathway of sugar puckering between the C20-endo and C30-endo conformations of deoxyadenosine (dA) is reported using the stochastic difference equation (SDE) algorithm, which approximates longtime pathways. The south pucker is favored over the north by 0.34 0.2 kcal/mol, and the free energy barrier is about 2.2 0.2 kcal/mol above the global minimum. The transition o...

Different techniques like "closed loop stripping" [CLSA], "purge and trap" [PTI], and continuous steam distillation extraction [SDE] were used to establish GC profiles of major histocompatibility complex-associated volatile constituents of human urine and statistically evaluated for reliability. Of the three methods investigated, PTI appeared to be superior for the detection of very volatile su...

In this paper we discuss the stochastic differential equation (SDE) susceptibleinfected-susceptible (SIS) epidemic model with demographic stochasticity. First we prove that the SDE has a unique nonnegative solution which is bounded above. Then we give conditions needed for the solution to become extinct. Next we use the Feller test to calculate the respective probabilities of the solution first...

Stability is the most relevant property of dynamical systems. The stability stochastic differential equations a challenging and still open problem. In this article, using fuzzy Mittag–Leffler function, we introduce new controller function to stabilize equation (SDE) ν′(γ,μ)=Fγ,μ,ν(γ,μ). By adopting fixed point technique, are able prove Mittag–Leffler–Hyers–Ulam–Rassias SDE.

‎In this work we prove Malliavin differentiability for the solution to an SDE with locally Lipschitz and semi-monotone drift‎. ‎To prove this formula‎, ‎we construct a sequence of SDEs with globally Lipschitz drifts and show that the $p$-moments of their Malliavin derivatives are uniformly bounded‎.

A new algorithm of determination of coe cients of multidimensional heat equations on the basis of temperature measurements is proposed. A system of stochastic di erential equations (SDE) can be assigned to a linear multidimensional heat equation. The solution of the heat equation can be obtained by solving the corresponding SDE by the method of statistical modeling. The sensitivity analysis is ...