Séminaire de Probabilités XL

Laure Coutin (auth.), Catherine Donati-Martin, Michel Émery, Alain Rouault, Christophe Stricker (eds.)9783540711889, 3540711880

Two noteworthy features of the 40th volume of the Séminaire de Probabilités are L. Coutin’s advanced course on calculus driven by fractional Brownian motion, and a series of seven interrelated works on local time-space calculus. Other topics from stochastic processes and stochastic finance include three contributions by A.S. Cherny on general approaches to arbitrage pricing.

Table of contents :
Front Matter….Pages I-XI
Front Matter….Pages 1-1
An Introduction to (Stochastic) Calculus with Respect to Fractional Brownian Motion….Pages 3-65
Front Matter….Pages 67-67
A Change-of-Variable Formula with Local Time on Surfaces….Pages 70-96
A Note on a Change of Variable Formula with Local Time-Space for Lévy Processes of Bounded Variation….Pages 97-104
Integration with Respect to Self-Intersection Local Time of a One-Dimensional Brownian Motion….Pages 105-116
Generalized Itǒ Formulae and Space-Time Lebesgue–Stieltjes Integrals of Local Times….Pages 117-136
Local Time-Space Calculus for Reversible Semimartingales….Pages 137-146
Elements of Stochastic Calculus via Regularization….Pages 147-185
On the Smooth-Fit Property for One-Dimensional Optimal Switching Problem….Pages 187-199
Front Matter….Pages 201-201
A Strong Form of Stable Convergence….Pages 203-225
Product of Harmonic Maps is Harmonic: A Stochastic Approach….Pages 227-233
More Hypercontractive Bounds for Deformed Orthogonal Polynomial Ensembles….Pages 235-240
No Multiple Collisions for Mutually Repelling Brownian Particles….Pages 241-246
On the Joint Law of the L1 and L2 Norms of a 3-Dimensional Bessel Bridge….Pages 247-264
Tanaka Formula for Symmetric Lévy Processes….Pages 265-285
An Excursion-Theoretical Approach to Some Boundary Crossing Problems and the Skorokhod Embedding for Reflected Lévy Processes….Pages 287-307
The Maximality Principle Revisited: On Certain Optimal Stopping Problems….Pages 309-328
Correlated Processes and the Composition of Generators….Pages 329-342
Representation of the Martingales for the Brownian Snake….Pages 343-354
Discrete Sampling of Functionals of Ito Processes….Pages 355-374
Ito’s Integrated Formula for Strict Local Martingales with Jumps….Pages 375-388
Front Matter….Pages 201-201
Enlargement of Filtrations and Continuous Girsanov-Type Embeddings….Pages 389-410
On a Lemma by Ansel and Stricker….Pages 411-414
General Arbitrage Pricing Model: I – Probability Approach….Pages 415-445
General Arbitrage Pricing Model: II – Transaction Costs….Pages 447-461
General Arbitrage Pricing Model: III – Possibility Approach….Pages 463-481