確率論覚え書き on Ippei Obayashi's Websitehttps://i-obayashi.info/math_memo/probability_theory/Recent content in 確率論覚え書き on Ippei Obayashi's WebsiteHugo -- gohugo.ioenobayashi@okayama-u.ac.jp (Ippei Obayashi)obayashi@okayama-u.ac.jp (Ippei Obayashi)© 2026 Ippei Obayashi2つの確率変数が一致する条件https://i-obayashi.info/math_memo/probability_theory/identity_of_two_random_variables/Mon, 01 Jan 0001 00:00:00 +0000obayashi@okayama-u.ac.jp (Ippei Obayashi)https://i-obayashi.info/math_memo/probability_theory/identity_of_two_random_variables/π-λ 定理https://i-obayashi.info/math_memo/probability_theory/pi_lambda_theorem/Mon, 01 Jan 0001 00:00:00 +0000obayashi@okayama-u.ac.jp (Ippei Obayashi)https://i-obayashi.info/math_memo/probability_theory/pi_lambda_theorem/確率変数が生成するσ-代数https://i-obayashi.info/math_memo/probability_theory/sigma_algebra_generated_by_random_variable/Mon, 01 Jan 0001 00:00:00 +0000obayashi@okayama-u.ac.jp (Ippei Obayashi)https://i-obayashi.info/math_memo/probability_theory/sigma_algebra_generated_by_random_variable/複数の確率変数で生成されるσ-代数https://i-obayashi.info/math_memo/probability_theory/sigma_algebra_generated_by_multiple_random_variables/Mon, 01 Jan 0001 00:00:00 +0000obayashi@okayama-u.ac.jp (Ippei Obayashi)https://i-obayashi.info/math_memo/probability_theory/sigma_algebra_generated_by_multiple_random_variables/条件付き期待値の定義https://i-obayashi.info/math_memo/probability_theory/conditional_expectation/Mon, 01 Jan 0001 00:00:00 +0000obayashi@okayama-u.ac.jp (Ippei Obayashi)https://i-obayashi.info/math_memo/probability_theory/conditional_expectation/条件付き期待値の線形性https://i-obayashi.info/math_memo/probability_theory/linearity_of_conditional_expectation/Mon, 01 Jan 0001 00:00:00 +0000obayashi@okayama-u.ac.jp (Ippei Obayashi)https://i-obayashi.info/math_memo/probability_theory/linearity_of_conditional_expectation/定値確率変数の条件付き期待値は定値https://i-obayashi.info/math_memo/probability_theory/conditional_expectation_of_constant_random_variable/Mon, 01 Jan 0001 00:00:00 +0000obayashi@okayama-u.ac.jp (Ippei Obayashi)https://i-obayashi.info/math_memo/probability_theory/conditional_expectation_of_constant_random_variable/条件付き期待値の条件付き期待値https://i-obayashi.info/math_memo/probability_theory/conditional_expectation_of_conditional_expectation/Mon, 01 Jan 0001 00:00:00 +0000obayashi@okayama-u.ac.jp (Ippei Obayashi)https://i-obayashi.info/math_memo/probability_theory/conditional_expectation_of_conditional_expectation/条件付き期待値の順序の保存https://i-obayashi.info/math_memo/probability_theory/preserving_the_order_of_conditional_expectation/Mon, 01 Jan 0001 00:00:00 +0000obayashi@okayama-u.ac.jp (Ippei Obayashi)https://i-obayashi.info/math_memo/probability_theory/preserving_the_order_of_conditional_expectation/条件付き期待値の単調収束定理https://i-obayashi.info/math_memo/probability_theory/monotone_convergence_theorem_on_conditional_expectation/Mon, 01 Jan 0001 00:00:00 +0000obayashi@okayama-u.ac.jp (Ippei Obayashi)https://i-obayashi.info/math_memo/probability_theory/monotone_convergence_theorem_on_conditional_expectation/G-可測な確率変数の条件付き期待値https://i-obayashi.info/math_memo/probability_theory/identity_on_conditional_expectation_of_conditional_expectation/Mon, 01 Jan 0001 00:00:00 +0000obayashi@okayama-u.ac.jp (Ippei Obayashi)https://i-obayashi.info/math_memo/probability_theory/identity_on_conditional_expectation_of_conditional_expectation/分割から生成されるσ-代数に対する条件付き期待値https://i-obayashi.info/math_memo/probability_theory/conditional_expectation_on_a_partition/Mon, 01 Jan 0001 00:00:00 +0000obayashi@okayama-u.ac.jp (Ippei Obayashi)https://i-obayashi.info/math_memo/probability_theory/conditional_expectation_on_a_partition/条件付き確率https://i-obayashi.info/math_memo/probability_theory/conditional_probability/Mon, 01 Jan 0001 00:00:00 +0000obayashi@okayama-u.ac.jp (Ippei Obayashi)https://i-obayashi.info/math_memo/probability_theory/conditional_probability/部分σ-代数に対する条件付き確率の妥当性https://i-obayashi.info/math_memo/probability_theory/validity_of_conditional_probability/Mon, 01 Jan 0001 00:00:00 +0000obayashi@okayama-u.ac.jp (Ippei Obayashi)https://i-obayashi.info/math_memo/probability_theory/validity_of_conditional_probability/確率変数が生成するσ-代数による条件付き期待値https://i-obayashi.info/math_memo/probability_theory/conditional_expectation_on_a_sigma_algebra_generated_by_random_variable/Mon, 01 Jan 0001 00:00:00 +0000obayashi@okayama-u.ac.jp (Ippei Obayashi)https://i-obayashi.info/math_memo/probability_theory/conditional_expectation_on_a_sigma_algebra_generated_by_random_variable/ドゥーブ・ディンキンの補題https://i-obayashi.info/math_memo/probability_theory/doob_dynkin_lemma/Mon, 01 Jan 0001 00:00:00 +0000obayashi@okayama-u.ac.jp (Ippei Obayashi)https://i-obayashi.info/math_memo/probability_theory/doob_dynkin_lemma/期待値のL2内積と条件付き期待値https://i-obayashi.info/math_memo/probability_theory/l2_inner_product_and_conditional_expectation/Mon, 01 Jan 0001 00:00:00 +0000obayashi@okayama-u.ac.jp (Ippei Obayashi)https://i-obayashi.info/math_memo/probability_theory/l2_inner_product_and_conditional_expectation/確率変数の独立性と条件付き期待値https://i-obayashi.info/math_memo/probability_theory/independence_of_random_variables_and_conditional_expectation/Mon, 01 Jan 0001 00:00:00 +0000obayashi@okayama-u.ac.jp (Ippei Obayashi)https://i-obayashi.info/math_memo/probability_theory/independence_of_random_variables_and_conditional_expectation/確率変数の交換可能性https://i-obayashi.info/math_memo/probability_theory/exchangeability/Mon, 01 Jan 0001 00:00:00 +0000obayashi@okayama-u.ac.jp (Ippei Obayashi)https://i-obayashi.info/math_memo/probability_theory/exchangeability/交換可能σ-代数https://i-obayashi.info/math_memo/probability_theory/exchangeable_sigma_algebra/Mon, 01 Jan 0001 00:00:00 +0000obayashi@okayama-u.ac.jp (Ippei Obayashi)https://i-obayashi.info/math_memo/probability_theory/exchangeable_sigma_algebra/フィルトレーションhttps://i-obayashi.info/math_memo/probability_theory/filtration/Mon, 01 Jan 0001 00:00:00 +0000obayashi@okayama-u.ac.jp (Ippei Obayashi)https://i-obayashi.info/math_memo/probability_theory/filtration/マルチンゲールhttps://i-obayashi.info/math_memo/probability_theory/martingale/Mon, 01 Jan 0001 00:00:00 +0000obayashi@okayama-u.ac.jp (Ippei Obayashi)https://i-obayashi.info/math_memo/probability_theory/martingale/逆マルチンゲールhttps://i-obayashi.info/math_memo/probability_theory/reverse_martingale/Mon, 01 Jan 0001 00:00:00 +0000obayashi@okayama-u.ac.jp (Ippei Obayashi)https://i-obayashi.info/math_memo/probability_theory/reverse_martingale/停止時刻https://i-obayashi.info/math_memo/probability_theory/stopping_time/Mon, 01 Jan 0001 00:00:00 +0000obayashi@okayama-u.ac.jp (Ippei Obayashi)https://i-obayashi.info/math_memo/probability_theory/stopping_time/