Basic Stochastic Processes by Zdzisław Brzeźniak and Tomasz Zastawniak Springer-Verlag, London 1999 Corrections in the 1st printing

Version: 21 May 2005 Page and line numbers refer to the 1st printing of the book. A list of corrections in the 2nd printing is also available. Please see

http://www-users.york.ac.uk/~tz506/bsp

To make a comment or report further mistakes please contact the authors at

bz506@york.ac.uk or tz506@york.ac.uk

Your feedback will be greatly appreciated!

vii_{3} with discrete time should be in discrete time 8_{9} P (A) = P (A|B_{1})+P (A|B_{2})+⋯ should be P (A) = P (A|B_{1})P (B_{1})+

P (A|B_{2})P (B_{2}) + ⋯ 13_{2} P {η ≥ t} should be P {η ≤ t} 17^{5} This chapter is been designed should be This chapter is designed 24_{13} 0 ∉ C should be 2 ∉ C 24_{12} 0 ∈ C should be 2 ∈ C

29_{8} η should be ζ

30^{3} if ξ is a step function should be if ξ is a G-measurable step function 38^{1} E(ξ|η) should be E(ξ^{2}|η) 38_{8} E(ξ|η) should be E(ξ^{2}|η)

41^{9} ξ should be ζ
41^{11} ξ should be ζ

59_{5} ⋂_{n=1}^{∞} P {τ > 2Kn} should be P ( ⋂_{n=1}^{∞}{τ > 2Kn})

60^{8} replace 2) by 1)

60^{3} ∑_{n=1}^{∞} should be ∑_{n=0}^{∞}

60^{4} ∑_{n=1}^{∞} should be ∑_{n=0}^{∞}

60^{5} ∑_{n=1}^{∞} should be ∑_{n=0}^{∞}

68_{11} Eξ_{τ} should be E(ξ_{τ})

68_{11} insert . at the end of the displayed equation

68_{8} Eξ_{τ} should be E(ξ_{τ}) 96^{6} Elschenbiden should be Elschenbieden 97^{12} ϕ(0) = 0 should be ϕ(0) = 1 100^{8} Elschenbiden should be Elschenbieden 111^{3} π := ∑_{j∈S} π_{j}δ_{j} should be μ := ∑_{j∈S} π_{j}δ_{j} 113^{10} delete recurrent

115_{10} π_{j} ∑_{s∈S} π_{j}p_{r}(s|i) should be π_{j} ∑_{s∈S} p_{r}(s|i)

146_{4} P {η_{1} > s} ⋯ P {η_{k} > s} should be P {η_{1} > s_{1}} ⋯ P {η_{k} > s_{k}} 146_{2} P {η_{1} > s} ⋯ P {η_{k} > s} should be P {η_{1} > s_{1}} ⋯ P {η_{k} > s_{k}} 165_{11} P {η_{1} > s} ⋯ P {η_{k} > s} should be P {η_{1} > s_{1}} ⋯ P {η_{k} > s_{k}} 165_{6} P {η_{1} > s} ⋯ P {η_{k} > s} should be P {η_{1} > s_{1}} ⋯ P {η_{k} > s_{k}} 165_{2} P {η_{1} > s} ⋯ P {η_{k} > s} should be P {η_{1} > s_{1}} ⋯ P {η_{k} > s_{k}} 187_{7} We claim that should be by Jensen’s inequality. We claim that 190^{1} from definition should be from the definition 190^{8} from definition should be from the definition 191_{14} This has been proved in Proposition 7.1. should be This follows by

approximating 1_{[0,t)}f by random step processes in M_{step}^{2} and using Proposition 7.1.

195_{7} is an Itô process. should be is an Itô process; see Exercise 7.8. 196^{9,10} the latter should be which

202^{8} of all functions should be in all functions 203^{15} is a solution of should be satisfies 203^{15} clearly satisfies should be also satisfies 214_{2} , since should be , since by the Cauchy-Schwartz inequality

215^{2,3,4} lines 2,3,4 should be replaced by

≤ n ∑_{i=0}^{n−1} E (|∫_{t_{i}^{n}}^{t_{i+1}^{n}} (W (t_{i+1}^{n}) − W (t)) dt|^{2})

≤ n ∑_{i=0}^{n−1} (t_{i+1}^{n} − t_{i}^{n}) E (∫_{t_{i}^{n}}^{t_{i+1}^{n}} |W (t_{i+1}^{n}) − W (t)|^{2} dt)

= n ∑_{i=0}^{n−1} \frac{(t_{i+1}^{n} − t_{i}^{n})^{3}}{2} = n ∑_{i=0}^{n−1} \frac{T^{3}}{2n^{3}} = \frac{T^{3}}{2n} → 0 as n → ∞.