Related papers: A converse comparison theorem for backward stochas…
This work develops Monte Carlo Euler adaptive time stepping methods for the weak approximation problem of jump diffusion driven stochastic differential equations. The main result is the derivation of a new expansion for the omputational…
In the present paper, we have developed a method for solving \textit{diophantine inequalities} using their relationship with the \textit{difference between consecutive primes}. Using this approach we have been able to prove some theorems,…
Deformed logarithms and their inverse functions, the deformed exponentials, are important tools in the theory of non-additive entropies and non-extensive statistical mechanics. We formulate and prove counterparts of Golden-Thompson's trace…
Results on the existence, uniqueness and strict comparison for solutions to a BSDE driven by a multi-dimensional RCLL martingale are established. The goal is to develop a general multi-asset framework encompassing a wide spectrum of…
In this paper we discuss backward stochastic differential equations with Markov chain noise, having continuous drivers. We obtain the existence of a solution which is possibly not unique. Moreover, we show there is a minimal solution for…
The present paper is devoted to the study of diagonally quadratic backward stochastic differential equation with oblique reflection. Using a penalization approach, we show the existence fo a solution by providing some delicated a priori…
This work concerns about forward-backward multivalued stochastic systems. First of all, we prove one average principle for general stochastic differential equations in the $L^{2p}$ ($p\geq 1$) sense. Moreover, for $p=1$ a convergence rate…
Quantum trajectory theories have not fully reconciled discrete quantum jumps with continuous unitary evolution. We address this challenge by developing a hidden variable formulation that reveals hidden correlations in individual trials. We…
In this paper we study the strong convergence for the Euler-Maruyama approximation of a class of stochastic differential equations whose both drift and diffusion coefficients are possibly discontinuous.
We develop a general technique for proving convergence of repeated quantum interactions to the solution of a quantum stochastic differential equation. The wide applicability of the method is illustrated in a variety of examples. Our main…
This paper is concerned with the quasi-linear reflected backward stochastic partial differential equation (RBSPDE for short). Basing on the theory of backward stochastic partial differential equation and the parabolic capacity and…
In this work the existence of solutions of one-dimensional backward dou- bly stochastic differential equations (BDSDEs in short) where the coefficient is left-Lipschitz in y (may be discontinuous) and Lipschitz in z is studied. Also, the…
Neural stochastic differential equation model with a Brownian motion term can capture epistemic uncertainty of deep neural network from the perspective of a dynamical system. The goal of this paper is to improve the convergence rate of the…
In this paper we introduce a class of forward-backward stochastic differential equations on tensor fields of Riemannian manifolds, which are related to semi-linear parabolic partial differential equations on tensor fields. Moreover, we will…
We show a reverse isoperimetric inequality within the class of relative outer parallel bodies, with respect to a general convex body $E$, along with its equality condition. Based on the convexity of the sequence of quermassintegrals of…
Many time series are effectively generated by a combination of deterministic continuous flows along with discrete jumps sparked by stochastic events. However, we usually do not have the equation of motion describing the flows, or how they…
The numerical solution of an ordinary differential equation can be interpreted as the exact solution of a nearby modified equation. Investigating the behaviour of numerical solutions by analysing the modified equation is known as backward…
In the paper, stationary measures of stochastic differential equations with jumps are considered. Under some general conditions, existence of stationary measures is proved through Markov measures and Lyapunov functions. Moreover, for two…
In this paper, we investigate the optimal control problems for stochastic differential equations (SDEs in short) of mean-field type with jump processes. The control variable is allowed to enter into both diffusion and jump terms. This…
This work belongs to the framework of inverse problems with linear model. The resolution of this type of problem consists in minimizing (possibly under constraints) a function of discrepancy between the measurements and a physical model of…