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In this paper we discuss weak convergence of continuous-time Markov chains to a non-symmetric pure jump process. We approach this problem using Dirichlet forms as well as semimartingales. As an application, we discuss how to approximate a given Markov process by Markov chains. [ABSTRACT FROM AUTHOR]

We prove that a fork-convex family $$ \mathbb{W} $$ of nonnegative stochastic processes has an equivalent supermartingale density if and only if the set H of nonnegative random variables majorized by the values of elements of $$ \mathbb{W} $$ at fixed instants of time is bounded in probability. A securities market model with arbitrarily many main risky assets, specified by the set $$ \mathbb{W}\left( \mathbb{S} \right) $$ of nonnegative stochastic integrals with respect to finite collections of semimartingales from an arbitrary indexed family S, satisfies the assumptions of this theorem. [ABSTRACT FROM AUTHOR]

We prove that a sequence of diffusion processes in ℝ n that are Brownian motions with drift unboundedly increasing in modulus and directed to a manifold converges in distribution to the Brownian motion on the manifold. [ABSTRACT FROM AUTHOR]

We consider the mean-variance hedging problem under partial information in the case where the flow of observable events does not contain the full information on the underlying asset price process. We introduce a certain type martingale equation and characterize the optimal strategy in terms of the solution of this equation. We give relations between this equation and backward stochastic differential equations for the value process of the problem. [ABSTRACT FROM AUTHOR]