Displaying similar documents to “Stochastic process measurability conditions”

The d X ( t ) = X b ( X ) d t + X σ ( X ) d W equation and financial mathematics. I

Josef Štěpán, Petr Dostál (2003)

Kybernetika

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The existence of a weak solution and the uniqueness in law are assumed for the equation, the coefficients b and σ being generally C ( ℝ + ) -progressive processes. Any weak solution X is called a ( b , σ ) -stock price and Girsanov Theorem jointly with the DDS Theorem on time changed martingales are applied to establish the probability distribution μ σ of X in C ( ℝ + ) in the special case of a diffusion volatility σ ( X , t ) = σ ˜ ( X ( t ) ) . A martingale option pricing method is presented.

Brownian representations of cylindrical local martingales, martingale problem and strong Markov property of weak solutions of SPDEs in Banach spaces

Martin Ondreját (2005)

Czechoslovak Mathematical Journal

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The paper deals with three issues. First we show a sufficient condition for a cylindrical local martingale to be a stochastic integral with respect to a cylindrical Wiener process. Secondly, we state an infinite dimensional version of the martingale problem of Stroock and Varadhan, and finally we apply the results to show that a weak existence plus uniqueness in law for deterministic initial conditions for an abstract stochastic evolution equation in a Banach space implies the strong...