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Exponential ergodicity of semilinear equations driven by Lévy processes in Hilbert spaces

Anna Chojnowska-Michalik, Beniamin Goldys (2015)

Banach Center Publications

We study convergence to the invariant measure for a class of semilinear stochastic evolution equations driven by Lévy noise, including the case of cylindrical noise. For a certain class of equations we prove the exponential rate of convergence in the norm of total variation. Our general result is applied to a number of specific equations driven by cylindrical symmetric α-stable noise and/or cylindrical Wiener noise. We also consider the case of a "singular" Wiener process with unbounded covariance...

Exponential martingales and CIR model

Wojciech Szatzschneider (2008)

Banach Center Publications

With the use of exponential martingales and the Girsanov theorem we show how to calculate bond prices in a large variety of square root processes. We clarify and correct several errors that abound in financial literature concerning these processes. The most important topics are linear risk premia, the Longstaff double square model, and calculations concerning correlated CIR processes.

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